A note on stability and NIP in one variable
Pierre Simon
TL;DR
This paper discusses the relationship between stability and NIP properties in model theory, focusing on formulas with two variables and their implications for the classification of theories.
Contribution
It establishes an equivalence between NIP/stability of a theory and the NIP/stability of formulas with two variables, clarifying the role of single-variable formulas.
Findings
NIP and stability can be characterized by formulas with two variables.
The paper provides a criterion linking properties of formulas with one and two variables.
It offers insights into the structure of theories based on variable restrictions.
Abstract
A theory is NIP (resp. stable) if and only if every formula with parameters in two single variables is NIP (resp. does not have the order property).
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Taxonomy
TopicsAdvanced Topology and Set Theory · Functional Equations Stability Results · Advanced Algebra and Logic